The optical performance of pairs of toroidal mirrors in grazing incidence has been studied analytically and numerically. Two types of toroidal surface are possible: football and bicycle tire. In grazing incidence and for configurations that compensate up to second-order aberrations, there are significant differences in performance between the two types. For football-type tori the best configuration appears to be Z-shaped with tangential and sagittal foci at the middle point between the mirrors. For bicycle tire-type tori the best configuration is U-shaped with the tangential focus at the middle point and the sagittal at infinity.
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